[ 기초수학| JAVA ] - 점화식과 재귀함수 < Recurrence relation / Recursive Function >

 

점화식과 재귀함수

< Recurrence relation / Recursive Function >

 

- Recursion means  "defining a problem in terms of itself".

 

- For example, the Fibonacci sequence is defined as: F(i) = F(i-1) + F(i-2)

 

-The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. 

 

 

 

System.out.println(" [ 점화식과 재귀함수 ] ");

// 1,3,9,27, ... 의 n번째 수
int n = 4;
int result = 1;
for(int i = 0; i < n; i++);
{
	if(i == 0)
    {
    	result = 1; 
    }else
    {
    	result *= 3;
    }
}
System.out.println(result);

// recursive method1 
static int recursion1(int n)
{
	if(n ==1)
    {
    	return 1;
    }
	return 3 * recursion1(n-1); // 3 * recursion1(3) * recursion1(2) * recursion1(1) 
}


// 1,2,3,4,5,6, ... 의 n번째까지의 합
n = 5;
result = 0;
for(int i = 1; i < n +1; i++)
{
	result += i;
}
System.out.println(result);

// recursive method2
static int recursion2(int n)
{
	if(n == 1)
    {
    	return 1;
    }
    return n + recursion2(n-1); 
}


// 피보나치 수열 - 1,1,2,3,5,8,13,...의 n번째 수
n = 6;
result = 0;
int a1 = 1;
int a2 = 1;

if(n < 3){
	result = 1;
}else{
	for(int i = 2; i < n; i++)
	{
    	result = a1 + a2;
        a1 = a2;
        a2 = result;
    }
}
System.out.println(result);

// recursive method3
static int recursion3(int n)
{
	if(n <3){
    	return 1;
  	}
    return recursion3(n-2) + recursion3(n-1);
}